Pricing a European Basket Option in the Presence of Proportional Transaction Costs

C. Atkinson and C. A. Alexandropoulos

Applied Mathematical Finance, 2006, vol. 13, issue 3, 191-214

Abstract: A crucial assumption in the Black-Scholes theory of options pricing is the no transaction costs assumption. However, following such a strategy in the presence of transaction costs would lead to immediate ruin. This paper presents a stochastic control approach to the pricing and hedging of a European basket option, dependent on primitive assets whose prices are modelled as lognormal diffusions, in the presence of costs proportional to the size of the transaction. Under certain assumptions on the individual preferences, it is able to reduce the dimensionality of the resulting control problem. This facilitates considerably the study of the value function and the characterisation of the optimal trading policy. For solution of the problem a perturbation analysis scheme is utilized to derive a non-trivial, asymptotically optimal result. The findings reveal that this result can be expressed by means of a small correction to the corresponding solution of the frictionless Black-Scholes type problem, resembling a multi-dimensional 'bandwidth' around the vanilla case, which, moreover, is readily tractable.

Keywords: Option pricing; transaction costs; utility function; asymptotic expansion; Hamilton-Jacobi-Bellman equation; closed form solution (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.tandfonline.com/doi/abs/10.1080/13504860600563184 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:apmtfi:v:13:y:2006:i:3:p:191-214

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RAMF20

DOI: 10.1080/13504860600563184

Access Statistics for this article

Applied Mathematical Finance is currently edited by Professor Ben Hambly and Christoph Reisinger

More articles in Applied Mathematical Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().